NEW ORLEANS — It’s a question that will be answered in time, as Celtics president of basketball operations Danny Ainge accumulates assets, collects expiring contracts, and desperately protects salary-cap space.

The recent resurrection of the Celtics, which produced two trips to the NBA Finals and one championship, was borne through trade. Ray Allen was acquired on draft night in 2007 and Kevin Garnett was brought to Boston 33 days later.

Most of the free agents Boston has procured over the past two decades have either been players near the end of their careers looking for one last opportunity at a title, or moderately talented players. No premium free agent in recent memory has come to the Celtics, and there are many reasons.

The Celtics have not owned a plethora of salary-cap space over the past several years to accommodate a major free agent. Also, with the presence of players such as Garnett, Allen, Rajon Rondo, and Paul Pierce, there hasn’t been necessarily a need for a maximum player.

In the summer of 2015, the Celtics will have enough salary-cap space to acquire perhaps two maximum-salaried players, depending on whether Rondo and Jared Sullinger are signed to long-term extensions. Ainge will have the flexibility and opportunity to court a player in his prime, selling him on the tradition of the Celtics, the city of Boston, and life in the Northeast.

Will a premium free agent consider Boston, given that the last major free agent to come here was perhaps Xavier McDaniel in 1992?

A number of NBA current and former players at All-Star Weekend offered their opinions on Boston and the qualities they look for in choosing a team.

Minnesota forward Kevin Love, who can opt out of his contract following the 2015 season, said he is not as familiar with Boston as other road cities.

“I’ve never really spent much time in Boston. I don’t know it too well,” he said. “But I think as far as playing there, we love competing against those guys. I think they have a great coach and they have a ton of youngsters that are up-and-comers.

“Boston is a great city. I’m sure free agents would love to go there, especially with [Brad] Stevens as a coach. He’s a guy that can win basketball games. He gets guys to play for him. They’ve been having good success there, even in his first year, and he has a lot of young players. The coach has a lot to do with it, but yeah, Boston is a great place.”

What Stevens is accomplishing in Boston, building a culture, coaching an overachieving team, is being noticed around the league.

John Bazemore/AP/2012

Minnesota All-Star Kevin Love can opt out of his pact after the 2015 season.

As Doc Rivers sold the Celtics during his nine years as head coach in Boston, Stevens could be a critical factor in the decision of a free agent.

While weather, market size, and tradition are important, the team’s culture is also crucial, according Dwyane Wade, who decided to stay in Miami as a free agent in 2010.

“It’s a sports town, when it comes to hard-core fans, when it comes to the sport that you love being the biggest thing about a city, it’s one of the main attractions from that standpoint,” Wade said of Boston. “And the rich history, obviously. I don’t think [location] matters. As you see with Ray and KG, it was the right time for them. They were there and did some amazing things, so you never know.

“At the end of the day, you don’t get to spend as much time in [your home] city as you think you do. You’ve got to sell the culture of the organization. You’ve got to sell winning. You’ve got to sell personnel. Those things, to me, are important.

“Obviously, there’s certain cities that are not going to get the look of certain guys, that doesn’t mean only New York or only LA or only San Francisco, these cities are going to be the only ones to get these players. It’s selling your organization and what you’re trying to do, more than anything.”

Longtime Celtic and Boston resident Tom “Satch” Sanders said there remains an overall mystery about Boston that’s only solved by living here.

All-Stars such as Chris Paul admitted he didn’t know much about the city, although he said Rivers, despite leaving the club, revels in his time there.

Rick Fox, who spent the first six seasons with Boston and the last seven with the Lakers, said the unfamiliarity with Boston could be a factor in free agents’ decisions.

“If you know the history, you know the history of the organization, the commitment to excellence,’’ he said. “If you know the recent team that owns the organization now and their depth in business and knowledge of winning in life, then you’d want to be a part of that organization.

“It seems to me the pallet is wide open. It’s a blank slate outside of Rondo. I would think building from that starting point would be a lot easier than starting from other places.

“It’s a great city, man. It’s an amazing city. [People] have no idea and if I didn’t live there for six years and my son hadn’t grown up there, I wouldn’t have that experience myself, but I know it.”

What could help the Celtics’ pursuit of their next franchise cornerstone is their recent history, the fact Pierce, Garnett, and Allen enjoyed success in Boston, as well as appearing to cherish their time there.

“Boston had some down years, and somebody like Paul, I have to take my hat off to him because he dealt with it, stuck with it. And then they brought the conglomerate over there and you see what happened.”

And those tearful tributes to those players who return to Boston are being noticed by other players.

Kevin Durant said he became emotional when he watched the montages the Celtics put together for Pierce and Garnett last month.

“I was there when Perk [Kendrick Perkins] got his tribute and you can tell they love those guys much more than wins and losses,” Durant said. “As a player, you can definitely appreciate that.”